{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Modeling and Simulation in Python\n",
    "\n",
    "Chapter 8\n",
    "\n",
    "Copyright 2017 Allen Downey\n",
    "\n",
    "License: [Creative Commons Attribution 4.0 International](https://creativecommons.org/licenses/by/4.0)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Configure Jupyter so figures appear in the notebook\n",
    "%matplotlib inline\n",
    "\n",
    "# Configure Jupyter to display the assigned value after an assignment\n",
    "%config InteractiveShell.ast_node_interactivity='last_expr_or_assign'\n",
    "\n",
    "# import functions from the modsim.py module\n",
    "from modsim import *"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Functions from the previous chapter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_results(census, un, timeseries, title):\n",
    "    \"\"\"Plot the estimates and the model.\n",
    "    \n",
    "    census: TimeSeries of population estimates\n",
    "    un: TimeSeries of population estimates\n",
    "    timeseries: TimeSeries of simulation results\n",
    "    title: string\n",
    "    \"\"\"\n",
    "    plot(census, ':', label='US Census')\n",
    "    plot(un, '--', label='UN DESA')\n",
    "    plot(timeseries, color='gray', label='model')\n",
    "    \n",
    "    decorate(xlabel='Year', \n",
    "             ylabel='World population (billion)',\n",
    "             title=title)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def run_simulation(system, update_func):\n",
    "    \"\"\"Simulate the system using any update function.\n",
    "    \n",
    "    system: System object\n",
    "    update_func: function that computes the population next year\n",
    "    \n",
    "    returns: TimeSeries\n",
    "    \"\"\"\n",
    "    results = TimeSeries()\n",
    "    results[system.t_0] = system.p_0\n",
    "    \n",
    "    for t in linrange(system.t_0, system.t_end):\n",
    "        results[t+1] = update_func(results[t], t, system)\n",
    "        \n",
    "    return results"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Reading the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def read_table2(filename = 'data/World_population_estimates.html'):\n",
    "    tables = pd.read_html(filename, header=0, index_col=0, decimal='M')\n",
    "    table2 = tables[2]\n",
    "    table2.columns = ['census', 'prb', 'un', 'maddison', \n",
    "                  'hyde', 'tanton', 'biraben', 'mj', \n",
    "                  'thomlinson', 'durand', 'clark']\n",
    "    return table2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "#table2 = read_table2()\n",
    "#table2.to_csv('data/World_population_estimates2.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Year</th>\n",
       "      <th>census</th>\n",
       "      <th>prb</th>\n",
       "      <th>un</th>\n",
       "      <th>maddison</th>\n",
       "      <th>hyde</th>\n",
       "      <th>tanton</th>\n",
       "      <th>biraben</th>\n",
       "      <th>mj</th>\n",
       "      <th>thomlinson</th>\n",
       "      <th>durand</th>\n",
       "      <th>clark</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Year</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1950</th>\n",
       "      <td>1950</td>\n",
       "      <td>2557628654</td>\n",
       "      <td>2.516000e+09</td>\n",
       "      <td>2.525149e+09</td>\n",
       "      <td>2.544000e+09</td>\n",
       "      <td>2.527960e+09</td>\n",
       "      <td>2.400000e+09</td>\n",
       "      <td>2.527000e+09</td>\n",
       "      <td>2.500000e+09</td>\n",
       "      <td>2.400000e+09</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2.486000e+09</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1951</th>\n",
       "      <td>1951</td>\n",
       "      <td>2594939877</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2.572851e+09</td>\n",
       "      <td>2.571663e+09</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1952</th>\n",
       "      <td>1952</td>\n",
       "      <td>2636772306</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2.619292e+09</td>\n",
       "      <td>2.617949e+09</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1953</th>\n",
       "      <td>1953</td>\n",
       "      <td>2682053389</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2.665865e+09</td>\n",
       "      <td>2.665959e+09</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1954</th>\n",
       "      <td>1954</td>\n",
       "      <td>2730228104</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2.713172e+09</td>\n",
       "      <td>2.716927e+09</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      Year      census           prb            un      maddison  \\\n",
       "Year                                                               \n",
       "1950  1950  2557628654  2.516000e+09  2.525149e+09  2.544000e+09   \n",
       "1951  1951  2594939877           NaN  2.572851e+09  2.571663e+09   \n",
       "1952  1952  2636772306           NaN  2.619292e+09  2.617949e+09   \n",
       "1953  1953  2682053389           NaN  2.665865e+09  2.665959e+09   \n",
       "1954  1954  2730228104           NaN  2.713172e+09  2.716927e+09   \n",
       "\n",
       "              hyde        tanton       biraben            mj    thomlinson  \\\n",
       "Year                                                                         \n",
       "1950  2.527960e+09  2.400000e+09  2.527000e+09  2.500000e+09  2.400000e+09   \n",
       "1951           NaN           NaN           NaN           NaN           NaN   \n",
       "1952           NaN           NaN           NaN           NaN           NaN   \n",
       "1953           NaN           NaN           NaN           NaN           NaN   \n",
       "1954           NaN           NaN           NaN           NaN           NaN   \n",
       "\n",
       "     durand         clark  \n",
       "Year                       \n",
       "1950    NaN  2.486000e+09  \n",
       "1951    NaN           NaN  \n",
       "1952    NaN           NaN  \n",
       "1953    NaN           NaN  \n",
       "1954    NaN           NaN  "
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "table2 = pd.read_csv('data/World_population_estimates2.csv')\n",
    "table2.index = table2.Year\n",
    "table2.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "un = table2.un / 1e9\n",
    "census = table2.census / 1e9\n",
    "plot(census, ':', label='US Census')\n",
    "plot(un, '--', label='UN DESA')\n",
    "    \n",
    "decorate(xlabel='Year', \n",
    "             ylabel='World population (billion)',\n",
    "             title='Estimated world population')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Running the quadratic model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's the update function for the quadratic growth model with parameters `alpha` and `beta`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def update_func_quad(pop, t, system):\n",
    "    \"\"\"Update population based on a quadratic model.\n",
    "    \n",
    "    pop: current population in billions\n",
    "    t: what year it is\n",
    "    system: system object with model parameters\n",
    "    \"\"\"\n",
    "    net_growth = system.alpha * pop + system.beta * pop**2\n",
    "    return pop + net_growth"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Extract the starting time and population."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.557628654"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t_0 = get_first_label(census)\n",
    "t_end = get_last_label(census)\n",
    "p_0 = get_first_value(census)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Initialize the system object."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>values</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>t_0</th>\n",
       "      <td>1950.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>t_end</th>\n",
       "      <td>2016.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>p_0</th>\n",
       "      <td>2.557629</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>alpha</th>\n",
       "      <td>0.025000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>beta</th>\n",
       "      <td>-0.001800</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "t_0      1950.000000\n",
       "t_end    2016.000000\n",
       "p_0         2.557629\n",
       "alpha       0.025000\n",
       "beta       -0.001800\n",
       "dtype: float64"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "system = System(t_0=t_0, \n",
    "                t_end=t_end,\n",
    "                p_0=p_0,\n",
    "                alpha=0.025,\n",
    "                beta=-0.0018)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Run the model and plot results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "results = run_simulation(system, update_func_quad)\n",
    "plot_results(census, un, results, 'Quadratic model')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Generating projections"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To generate projections, all we have to do is change `t_end`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure to file figs/chap08-fig01.pdf\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "system.t_end = 2250\n",
    "results = run_simulation(system, update_func_quad)\n",
    "plot_results(census, un, results, 'World population projection')\n",
    "savefig('figs/chap08-fig01.pdf')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The population in the model converges on the equilibrium population, `-alpha/beta`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "13.856665141368708"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "results[system.t_end]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "13.88888888888889"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "-system.alpha / system.beta"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise:**  What happens if we start with an initial population above the carrying capacity, like 20 billion?  Run the model with initial populations between 1 and 20 billion, and plot the results on the same axes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "p0_array = linspace(1, 25, 11)\n",
    "\n",
    "for system.p_0 in p0_array:\n",
    "    results = run_simulation(system, update_func_quad)\n",
    "    plot(results)\n",
    "\n",
    "decorate(xlabel='Year',\n",
    "         ylabel='Population (billions)',\n",
    "         title='Projections with hypothetical starting populations')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Comparing projections"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can compare the projection from our model with projections produced by people who know what they are doing."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "def read_table3(filename = 'data/World_population_estimates.html'):\n",
    "    tables = pd.read_html(filename, header=0, index_col=0, decimal='M')\n",
    "    table3 = tables[3]\n",
    "    table3.columns = ['census', 'prb', 'un']\n",
    "    return table3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "#table3 = read_table3()\n",
    "#table3.to_csv('data/World_population_estimates3.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Year</th>\n",
       "      <th>census</th>\n",
       "      <th>prb</th>\n",
       "      <th>un</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Year</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2016</th>\n",
       "      <td>2016</td>\n",
       "      <td>7.334772e+09</td>\n",
       "      <td>NaN</td>\n",
       "      <td>7.432663e+09</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017</th>\n",
       "      <td>2017</td>\n",
       "      <td>7.412779e+09</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2018</th>\n",
       "      <td>2018</td>\n",
       "      <td>7.490428e+09</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2019</th>\n",
       "      <td>2019</td>\n",
       "      <td>7.567403e+09</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020</th>\n",
       "      <td>2020</td>\n",
       "      <td>7.643402e+09</td>\n",
       "      <td>NaN</td>\n",
       "      <td>7.758157e+09</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      Year        census  prb            un\n",
       "Year                                       \n",
       "2016  2016  7.334772e+09  NaN  7.432663e+09\n",
       "2017  2017  7.412779e+09  NaN           NaN\n",
       "2018  2018  7.490428e+09  NaN           NaN\n",
       "2019  2019  7.567403e+09  NaN           NaN\n",
       "2020  2020  7.643402e+09  NaN  7.758157e+09"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "table3 = pd.read_csv('data/World_population_estimates3.csv')\n",
    "table3.index = table3.Year\n",
    "table3.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`NaN` is a special value that represents missing data, in this case because some agencies did not publish projections for some years."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This function plots projections from the UN DESA and U.S. Census.  It uses `dropna` to remove the `NaN` values from each series before plotting it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_projections(table):\n",
    "    \"\"\"Plot world population projections.\n",
    "    \n",
    "    table: DataFrame with columns 'un' and 'census'\n",
    "    \"\"\"\n",
    "    census_proj = table.census / 1e9\n",
    "    un_proj = table.un / 1e9\n",
    "    \n",
    "    plot(census_proj.dropna(), ':', color='C0', label='US Census')\n",
    "    plot(un_proj.dropna(), '--', color='C1', label='UN DESA')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Run the model until 2100, which is as far as the other projections go."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>values</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>t_0</th>\n",
       "      <td>1950.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>t_end</th>\n",
       "      <td>2100.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>p_0</th>\n",
       "      <td>2.557629</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>alpha</th>\n",
       "      <td>0.025000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>beta</th>\n",
       "      <td>-0.001800</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "t_0      1950.000000\n",
       "t_end    2100.000000\n",
       "p_0         2.557629\n",
       "alpha       0.025000\n",
       "beta       -0.001800\n",
       "dtype: float64"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "system = System(t_0=t_0, \n",
    "                t_end=2100,\n",
    "                p_0=p_0,\n",
    "                alpha=0.025,\n",
    "                beta=-0.0018)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure to file figs/chap08-fig02.pdf\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "results = run_simulation(system, update_func_quad)\n",
    "\n",
    "plt.axvspan(1950, 2016, color='C0', alpha=0.05)\n",
    "plot_results(census, un, results, 'World population projections')\n",
    "plot_projections(table3)\n",
    "savefig('figs/chap08-fig02.pdf')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "People who know what they are doing expect the growth rate to decline more sharply than our model projects."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercises\n",
    "\n",
    "**Exercise:** The net growth rate of world population has been declining for several decades.  That observation suggests one more way to generate projections, by extrapolating observed changes in growth rate.\n",
    "\n",
    "The `modsim` library provides a function, `compute_rel_diff`, that computes relative differences of the elements in a sequence.\n",
    "\n",
    "Here's how we can use it to compute the relative differences in the `census` and `un` estimates:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "alpha_census = compute_rel_diff(census)\n",
    "plot(alpha_census, label='US Census')\n",
    "\n",
    "alpha_un = compute_rel_diff(un)\n",
    "plot(alpha_un, label='UN DESA')\n",
    "\n",
    "decorate(xlabel='Year', label='Net growth rate')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Other than a bump around 1990, net growth rate has been declining roughly linearly since 1965.  As an exercise, you can use this data to make a projection of world population until 2100.\n",
    "\n",
    "1. Define a function, `alpha_func`, that takes `t` as a parameter and returns an estimate of the net growth rate at time `t`, based on a linear function `alpha = intercept + slope * t`.  Choose values of `slope` and `intercept` to fit the observed net growth rates since 1965.\n",
    "\n",
    "2. Call your function with a range of `ts` from 1960 to 2020 and plot the results.\n",
    "\n",
    "3. Create a `System` object that includes `alpha_func` as a system variable.\n",
    "\n",
    "4. Define an update function that uses `alpha_func` to compute the net growth rate at the given time `t`.\n",
    "\n",
    "5. Test your update function with `t_0 = 1960` and `p_0 = census[t_0]`.\n",
    "\n",
    "6. Run a simulation from 1960 to 2100 with your update function, and plot the results.\n",
    "\n",
    "7. Compare your projections with those from the US Census and UN."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Solution\n",
    "\n",
    "def alpha_func(t):\n",
    "    intercept = 0.02\n",
    "    slope = -0.00021\n",
    "    return intercept + slope * (t - 1970)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "ts = linrange(1960, 2020)\n",
    "alpha_model = TimeSeries(alpha_func(ts), ts)\n",
    "plot(alpha_model, color='gray', label='model')\n",
    "plot(alpha_census)\n",
    "plot(alpha_un)\n",
    "\n",
    "decorate(xlabel='Year', ylabel='Net growth rate')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.043001508"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "t_0 = 1960\n",
    "t_end = 2100\n",
    "p_0 = census[t_0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>values</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>t_0</th>\n",
       "      <td>1960</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>t_end</th>\n",
       "      <td>2100</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>p_0</th>\n",
       "      <td>3.043</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>alpha_func</th>\n",
       "      <td>&lt;function alpha_func at 0x7ff92564ac80&gt;</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "t_0                                              1960\n",
       "t_end                                            2100\n",
       "p_0                                             3.043\n",
       "alpha_func    <function alpha_func at 0x7ff92564ac80>\n",
       "dtype: object"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "system = System(t_0=t_0, \n",
    "                t_end=t_end,\n",
    "                p_0=p_0,\n",
    "                alpha_func=alpha_func)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Solution\n",
    "\n",
    "def update_func_alpha(pop, t, system):\n",
    "    \"\"\"Update population based on a quadratic model.\n",
    "    \n",
    "    pop: current population in billions\n",
    "    t: what year it is\n",
    "    system: system object with model parameters\n",
    "    \"\"\"\n",
    "    net_growth = system.alpha_func(t) * pop\n",
    "    return pop + net_growth"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.1102518413268"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "update_func_alpha(p_0, t_0, system)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Solution\n",
    "\n",
    "results = run_simulation(system, update_func_alpha);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "plot_results(census, un, results, 'World population projections')\n",
    "plot_projections(table3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Related viewing:** You might be interested in this [video by Hans Rosling about the demographic changes we expect in this century](https://www.youtube.com/watch?v=ezVk1ahRF78)."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
